SPECIAL SERIES Part 4
Energy Risk & Markets
Default Retail Supply:
How to set reserve levels for full requirements auctions.
Last month, Risk Capital's Tom Brady identified numerous risk factors that should be considered when pricing load-following contracts. These risks included various temperature, load, and price risks that create enormous uncertainty around the cost to serve such commitments. This month, we present a method for estimating reserves for load and price risk using sophisticated modeling techniques. In addition, because all models have flaws, we present one approach for accounting for this model risk in the bid price.
The analysis presented uses historic examples from 2003 market price and load levels in the PJM region to demonstrate how bid prices can incorporate market price and model risk. We use the PSEG load market in 2003 as a basis for our discussion.
Typical Contract
Our initial example centers on estimating a bid price for a typical full-requirements contract. These contracts have a variable amount of demand. This deal has a historical load maximum of approximately 300 MW. A load servicer will enter a bid price that the customers will pay for the energy. The load servicer then must supply this energy at the prevailing spot price (assuming it does not have any other sources of owned generation or contractual supply). This contract is defined as serving the period from February 2003 through September 2003.
The first step of the bid-price process should be to determine the "zero-value price." That is, the bid one would expect to give in order to break even. In this example, the "zero value price" amounts to $42.19/MWh. Table 1 provides a summary of the average load to the customers and the related cost of that energy if the energy is supplied at the hourly spot price. Simply dividing the average cost of the energy supplied by the average load generates the bid price (Note: This approach assumes no discounting for simplicity).
Monte Carlo simulation was used to generate reasonable scenarios of load given different weather conditions. Each scenario also generates a different set of spot prices the load servicer would have to pay to serve this load. This analysis indicates that the load servicer should bid something greater than $42.19 to expect a positive net return. However, there is a tremendous amount of uncertainty around this estimate. Market risk and load-profile uncertainty generates $9.7 million in risk that cannot be ignored when bidding for the right to serve this load.
Table 2 provides a summary of the distribution of results from modeling a PSEG Full Requirements Contract in January of 2003.
The second step in the process is to determine the risk-adjusted bid price. There are a number of risks that should be considered in the bid price. The most significant include:
Load/Market Risk - quantified by the earnings at risk (EaR) of the transaction ($9.8 million in this example); Credit Risk - dependent on the customers and counterparties responsible for paying for the energy delivered. Auctions serve a diversified set of customers. Therefore, it is reasonable to assume the credit risk is insignificant. (If the bidder were to choose to reduce the Load/Market Risk, it would increase its credit risk); and
Model Risk - dependent on the models used. Running multiple back tests and parallel models can help to generate benchmark risk levels to cover this risk.A number of company specific factors also can affect the bid price:
Risk Appetite (target Risk Adjusted Return on Capital); Hedge strategy; and Risk profile of existing assets, loads, and other trades. Incorporating Market Risk Via RAROC
Risk Adjusted Return on Capital (RAROC) can be estimated with any Monte Carlo model using the expected value and risk numbers generated on a transaction. In its simplest form, RAROC=Expected Value/Risk. In our example above, the RAROC on the deal would be zero if the bid price was $42.19/MWh (Expected Net Earnings of $0/$9.8 million in EaR). Obviously, a 0 percent RAROC is not acceptable to most energy merchants. Therefore, a RAROC hurdle rate should be established depending on the organization's risk appetite.
25% $9.8 million x 0.25 = $2.45 million / 856 GWh = $2.86/MWh 50% $9.8 million x 0.50 = $4.9 million / 856 GWh = $5.72/MWh Add this premia to the "zero value bid price" of $42.19 to get the bid price adjusted for market risk (25%: $45.05/MWh, 50%: $47.92/MWh). Incorporating Model Risk Via RAROC
In addition, the bidder must acknowledge that every model has flaws and that the risk that the model does not include all risks properly must be incorporated in the bid price.
Model risk is the risk the model used to value the trade and measure the risk is materially different from the actual outcome. Monte Carlo models generate a distribution of outcomes. Assuming the analysis generates enough outcomes to cover all possible scenarios, the actual results should fall somewhere within the simulated distribution.
In the example below, we used a bid price of $44.09/MWh to perform our Model Risk analysis. Our model estimated that the value of the trade was expected to be $1.6 million (). The actual settled price was determined to be a $1.6 million loss. Based on the distribution of possible results, the actual settlement value fell within 0.61 standard deviations away from the expected value. This is considered well within acceptable limits.
It is not uncommon to hedge a trade like this. One can determine an "optimal" portfolio of forwards to use in hedging this trade, assuming it is appropriate to hedge the transaction as an isolated exposure. This optimal hedge results in different monthly amounts for on-peak and off-peak structures. Table 4 () compares the actual outcome to the modeled distributions of the hedge portfolio and the aggregate portfolio of the hedge and the load contract.
In this case, the hedge portfolio's actual net earnings of $2.6 million were 0.5 standard deviations away from the expected value around zero. However, the hedged portfolio was more than 2 standard deviations away from the expected value.
The duration of the trade has an impact on the model's accuracy. Monthly trades have no opportunity to "diversify the model risk across time." Monthly sigmas (listed in Table 5) on the hedged trade range from 0.26 to 14.64 for the PSEG example.
Clearly, an actual result that is 14.65 standard deviations away from the mean would provide some evidence that the model used to generate these results is not capturing all of the risks driving the ultimate profitability of the trade. As such, this information should be used to generate a "model risk" charge. We suggest implementing the following framework for generating a model risk charge:
Generate an "optimal" hedge portfolio; Use the duration of trade and the standard deviation of the earnings distribution to generate an overall model risk charge; and Translate that charge into $/MWh by dividing it by the expected load. Based on the detailed monthly analysis above, we have heuristically estimated a model-risk charge rule as follows:
For trades with delivery durations less than 9 months, use a sigma of 3; and For trades with delivery durations of more than 9 months, use a sigma of 15. This approach would generate a model risk charge of $894,000 on the PSEG trade. If this amount is divided by 856,772 MWh, a risk charge of $0.98/MWh would be added to the bid for model risk.
The recommended bid price on this trade should therefore be made up of four elements:
"Zero Value" base price: $42.19 Market Risk charge (25% RAROC): 2.86 Credit Risk charge (0 in this case): 0 Model risk charge (3 sigmas) 0.98 Total Bid price: $46.03. These risk charges should be added as specific charges on the trade so that the "extra value" of the higher bid price is not misinterpreted and recognized as profit. The charge for market risk could be returned as the trade is hedged successfully. However, an additional amount then would need to be charged for credit risk. The model-risk charge would remain in place and charged only if back testing results generate lower average sigmas. Table 6 illustrates the absolute cash amounts of these charges. The $2.86/Mwh charge translates to a $2.5 million risk charge while the $0.98/MWh generates an $840 million risk charge.
The analysis presented assumes the trade is being considered on a standalone basis. Future articles will explore possible reasons why a bid from two parties with very different existing risk profiles will generate different bid prices.
The charge for market risk can be reduced if an effective set of hedges are put in place. But why hedge? Is it not more attractive to leave this position open so that it can hedge the bidder's existing positions?
A more effective market-risk charge should consider the overall portfolio's risk and each transaction's contribution to that risk profile. This practice could allow for bid price that are actually below the market (if there is an incremental risk reduction to the portfolio).
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